The Gordon MP will serve alongside Robin Walker, the MP for Worcester, who is believed to be the first English MP to serve at the Scotland Office since the 19th century.
Mr Walker’s appointment on Friday was greeted with disbelief by Scottish Tory MPs, who expected jobs at Dover House to be filled from among their number.
One described their reaction as “stunned, baffled, incredulous”.
And SNP MP Pete Wishart described the decision as “a slap in the face for Ruth Davidson”.
Mr Walker was previously a Brexit minister and played a key behind-the-scenes role in talks with devolved administrations.
The Oxford educated MP is the son of Tory peer Peter Walker, who also represented Worcester in the Commons.
Mr Clark will also serve as a government whip.